Future Work

In future design work, designs with larger pitch and fewer turns such as antenna γ will be more robust. This is because the larger pitch is less influenced by variations in the trace width, and by having fewer turns the total conductor length is less influenced by shrinkage during firing. Alternatively, fabrication methods could be developed to

mitigate these variances.

Future work would include changing the number of turns in an attempt to manipulate the frequency that the lower-frequency peak occurs at and would include an attempt to manipulate the frequency of each of the peaks to merge them to obtain a higher electric field intensity than possible with either peak alone. Furthermore, future

simulations would use the entire thruster configuration to confirm the behavior of the antenna within the thruster design using start power measurements, as well as compare the experimental start power measurements vs. frequency with simulation results.

References

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[5] S. Liao, Microwave Electron-Tube Devices. Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1988.

[6] M. Lieberman and A. Lichtenberg, Principles of Plasma Discharges and

Materials Processing.: John Wiley & Sons, Inc., 2005.

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diagnostic package architecture and Deep Space One spacecraft event detection,"

[8] J.E. Polk, R.Y. Kakuda, J.R. Anderson, J.R. Brophy, V.K. Rawlin, M.J. Patterson, J. Sovey, and J. Hamley, "Validation of the NSTAR ion propulsion system on the deep space one mission: Overview and initial results," in Joint

Propulsion Conf., Los Angeles, CA, 1999, pp. AIAA-99-2274.

[9] D.L. Estublier, "The SMART-1 Spacecraft Potential Investigations," IEEE

Transactions on Plasma Science, vol. 36, no. 5, pp. 2262-2270, Oct. 2008.

[10] I.D. Boyd, "Numerical Simulation of Hall Thruster Plasma Plumes in Space," IEEE Transations on Plasma Science, vol. 34, no. 5, pp. 2140-2147, Oct. 2006.

[11] J. Hopwood, "Planar RF induction plasma coupling efficiency," Plasma

Sources Sci. Technol., vol. 3, no. 4, pp. 460-464, Nov. 1994.

[12] J. Hopwood, O. Minayeva, and Y. Yin, "Fabrication and characterization of a micromachined 5 mm inductively coupled plasma generator," J. Vac. Sci.

Technol. B, Microelectron. Nanometer Struct., vol. 18, no. 5, pp. 2446-2451, Sep

2000.

[13] J. Hopwood, "A microfabricated inductively coupled plasma generator," J.

Microelectromech. Syst., vol. 9, no. 3, pp. 309-313, Sep 2000.

[14] F. Iza and J. Hopwood, "Influence of operating frequency and coupling coefficient on the efficiency of microfabricated inductively coupled plasma sources," Plasma Sources Sci. Technol., vol. 11, no. 3, pp. 229-235, Aug 2002.

[15] R. Wirz, J. Polk, C. Marrese, J. Mueller, J. Escobedo, P. Sheehan,

"Development and Testing of a 3cm Electron Bombardment Micro-Ion Thruster,"

in 27th Int. Electric Propulsion Conf., Pasadena, CA, 2001, pp. IEPC-01-343.

[16] J. Taff, S. Shawver, M. Yates, C. Lee, J. Browning, D. Plumlee,

"Fabrication of an Inductively Coupled Plasma Antenna in Low Temperature Co- Fired Ceramic," International Journal of Applied Ceramic Technology, Feb 2012. [17] D. Plumlee, J. Steciak, A. Moll, "Development and Simulation of an

Embedded Hydrogen Peroxide Catalyst Chamber in Low-Temperature Co-Fired Ceramics," International Journal of Applied Ceramic Technology, vol. 4, no. 5, pp. 406-414, 2007.

[18] [Online]. http://www.comsol.com/

[19] A. Polycarpou, Introduction to the Finite Element Method in

Electromagnetics, 1st ed., Arizona State University Constantine A. Balanis, Ed.

United States of America: Morgan & Claypool, 2006.

[20] (2012) MATLAB The Language of Technical Computing. [Online]. http://www.mathworks.com/products/matlab/

[21] Constantine A. Balanis, Antenna Theory Analysis and Design, 3rd ed. Hoboken, New Jersey: John Wiley & Sons, 2005.

[22] J. Browning, C. Lee, D. Plumlee, S. Shawver, S. M. Loo, M. Yates, M. McCrink, J. Taff, "A Miniature Inductively Coupled Plasma Source for Ion Thrusters," IEEE Trans. Plasma Sci., vol. 39, no. 11, pp. 3187-3195, Nov. 2011.

[23] Agilent Technologies. (2008, June) [Online]. http://cp.literature.agilent.com/litweb/pdf/E4440-90618.pdf

APPENDIX A

EPROP Research Group

Figure A.1. EPROP Research Group. From left to right: Logan Knowles, Sonya Shawver (the author), Don Plumlee, Jim Browning, Matt McCrink, Sin Ming Loo, Carl Lee, Jack Woldtvedt, Inanc Senocak. The vacuum chamber is in between Drs.

Plumlee and Browning. Not pictured: Mallory Yates, Peter Bumbarger, Jesse Taff, Derek Reis, Kelci Parrish, Dr. Amy Moll.

APPENDIX B

COMSOL RF Simulation Model Development

The rf_coil tutorial module was used as a guide to create the COMSOL models presented in this thesis. The process followed to create the models is as follows.

Initiating Model

When creating a new model, the user is prompted to select the physics type and study type. Models all contain the following sections: Definitions, Geometry,

Materials, Physics, Mesh, Study, and Results. These options can be seen in Figure B1. Under each section features may be added. To see these options right click while

Figure B2. Example of right-clicking while hovering over “Geometry” to show the import option

Geometry and Selection

After importing the SolidWorks file, a sphere is added with a layer to act as the perfectly matched layer. Next, the work plane is selected and a rectangle added to become the lumped port as shown in Figure B3. Finally, a cylinder is added around the antenna to be simulated as LTCC.

Figure B3. Creating the rectangle to be used as the lumped port

Next an Explicit Selection was created, consisting of all the external boundaries on the SolidWorks import file. This selection was named Coil Surface.

Materials

The behavior of LTCC is added in the physics section, so only two materials were needed: air (defaulted to all domains), and a high conductivity material (copper). Copper was selected because it is a built-in material. Changing the conductivity to that of silver did not change the simulation results.

Physics

The Electromagnetic Waves section defaults to have one wave equation, perfect electric conductor boundaries, and initial values of zero. Another wave equation was added to this section, with a loss tangent displacement field model. It used a relative permittivity of 7.8 and a loss tangent of 0.006 as shown in Figure B4. Next, the outer boundaries of the sphere in the model were set to be Perfect Magnetic Conductors, and the sections that make the outer layer of the sphere were set to be Perfectly Matched Layers. The Lumped Port was also designated as the rectangle constructed earlier, set to Uniform, Cable, On, 1 V, and 50 Ω characteristic impedance as shown in Figure B5.

Figure B5. Lumped Port settings

Mesh

Finally, the design was meshed. A Free Tetrahedral mesh is used for every domain except for the outermost layer. The outermost layer is a swept mesh to ensure that the fields diminish properly in that region. In meshing, the goal was to achieve a mesh with less than 700,000 elements (the maximum solvable on the computer available) with reasonable quality as shown in Chapter 3. This required manipulating the size and other properties of the mesh for each domain. Oftentimes it was difficult to get the

geometry to mesh because of the fine features of the antenna relative to the overall geometry size, so trying many different mesh properties was required.

As a general rule, the “finer” the mesh selection, the smaller the minimum and maximum element sizes will be; the higher the resolution of narrow regions will be, and the lower the resolution of curvature will be. To obtain a mesh of reasonable size and quality for this project, a small element size is required with resolutions for a coarser mesh. An example showing one of the more difficult meshes (for antenna β) is shown in Figure B6.

Study and Results

Once the model was set, a Study was run to simulate the performance of the antenna for a range of frequencies. Then, a cut plane was created to show the intensities of the electric field vs. position. Data points were selected using Cut Point, and the data was exported. Figure B7 shows this portion of the process.

APPENDIX C

SolidWorks Antenna Model Development

Table C1: List of antennas simulated and fabricated

pitch (mm) # of turns α 0.9 5 β 0.78 8 γ 1.45 5

To create the SolidWorks model of the antenna, first a spiral trace was constructed using the Helix/Spiral tool. Next, a Sweep was performed using a cross- section and the spiral trace. From there, the ends of the spiral were cut down to known angles and the traces to each side were created. Finally, the completed model was imported to COMSOL as a solid part file.

APPENDIX D

MATLAB Code

%|| A Sonya Shawver & Peter Bumbarger Production || %|| ||

% ---

% Plots various Electric Fields of a Multi-turn spiral antenna modeled % by concentric loop antennas of constant current and varying phase

function E_phi=MATLABsimForThesis(iter,myfrac, radii)

range=0;

lfrac=.1*iter+myfrac;

%calculate circumferences from radii

c=2*pi.*radii; % Loop antenna circumferences [m]

lambda1=sum(c)/lfrac; % One full-wavelength (like 900MHz)

k1=(2*pi)/lambda1; % One wavelength wave number

%phase change

for n=1:length(radii)

p(n)=(c(n)*lfrac)*360/sum(c); % Loop antenna 1 one-wavelength phase

end

I_0=1; % Current through loop [A]

theta=linspace(0,2*pi); % Angle around the z-axis on the xy plane *MATLAB defines this angle

differently from Balanis

phi=linspace(-pi/2,pi/2); % Angle from the xy plane to the +z-axis *MATLAB defines this angle

differently from Balanis

[theta, phi]=meshgrid(theta, phi); % Creates meshgrid

r=0.01; % Observation distance from orign (small distances for near-field

approximation to work, r<<lambda) [m]

pshift=0;

E_phi=zeros(length(radii),100,100);

E_phi(n,:,:)=-

1i*((radii(n)/sum(c))^2*k1*sum(c)*I_0*(cosd(k1*r+pshift)-

1i*sind(k1*r+pshift)))/(4*r^2).*sin(phi); % The E-Field in the phi direction (Eqn.(5-26d) from Balanis p. 241)

pshift=pshift+p(n);

end % *Note that theta and phi have been switched within the equation to

agree with MATLAB's coordinate system

E_phi0=zeros(1,100,100); % These equations are using the electrical length of one wavelength

for n=1:length(radii)

E_phi0=E_phi0+E_phi(n,:,:); % Summation of the E-Fields of all the loop antennas

end

dim1=ceil((length(radii)+1)/2); dim2=ceil((length(radii)+1)/dim1);

subplot(2,5,iter) %simply gets rid of need for index 1 in (1,h,q)so sph2cart() may be applied

for h=1:100 for q=1:100 E_phi0_new(h,q)=E_phi0(1,h,q); end end %plot result [x0,y0,z0]=sph2cart(theta,phi, abs(E_phi0_new)); surf(x0,y0,z0,'EdgeColor','none') view([0,1,0]) axis([-30,30,-30,30,-50,50])

title(['\lambda ratio =',num2str(lfrac)],'FontWeight', 'bold','FontSize',13)